Basic push and pop
Input
run_ops([['push', 1], ['push', 2], ['pop'], ['pop'], ['empty']])
Output
[2, 1, True]
Push 1 then 2. pop returns 2 then 1. After both pops the stack is empty.
Full lesson preview
Design a stack using two queues
Implement a LIFO stack using two FIFO queues. Support push, pop, top, and empty operations.
Python practice24 minStacks & QueuesAdvancedLast updated March 27, 2026
Problem statement
You are asked to implement a stack data structure using exactly two queues. The stack should support the following operations:
- push(x): Push element x onto the stack.
- pop(): Remove and return the element on top of the stack. If the stack is empty, return None.
- top(): Return the top element without removing it. If the stack is empty, return None.
- empty(): Return True if the stack is empty, False otherwise.
Also provide a helper run_ops(ops) that executes a sequence of operations on a fresh stack instance and returns a list of results for operations that produce values (pop, top, empty).
Task
Build a stack using two queues and a helper runner to validate sequences of operations.
Examples
Input format
A list of operations. Each operation is a list where the first element is one of 'push', 'pop', 'top', 'empty'. 'push' includes a second element with the value.
Output format
A Python list of results (in order) for operations that return values: pop, top, and empty. Returned as a standard Python list.
Constraints
- Only use two queues (implemented as Python lists using append/pop(0) or collections style) for internal storage.
- pop and top should have amortized O(n) or O(1) as appropriate depending on design; aim for correct behavior.
- Do not use list methods that trivialize the queue abstraction like deque (explicit queue behavior via lists is fine).
- Provide run_ops helper used by tests.
Samples
Sample 1
Input
run_ops([['push', 5], ['top'], ['push', 6], ['top'], ['pop']])
Output
[5, 6, 6]
After pushing 5, top is 5. After pushing 6, top is 6. pop removes and returns 6.